ABSTRACT
Data traffic is the sequence of movement of data items through a point or a physical device. A typical data item is a contiguous sequence of bits forming a data packet. When these data items pass through a physical device, there is usually some impediment in the form of reception, processing, and forwarding. Such an impediment results in queuing and causes time delays. In general, queues have successive arrivals of customers as inputs. These arrivals experience possible waiting and service before being output as successive departures. This chapter introduces important random variables that constitute models for arrival and service disciplines. The statistical nature of arrivals can be expressed in different ways. For example, if successive interarrival times (IATs) are independent, a specification of the initial condition in the form of the time instant at which the operation of the queue starts and the probability density function (pdf) of IATs are sufficient to completely describe the nature of arrivals. The Pareto random variable for IATs is one such model. This random variable exhibits some important variations in its characteristics, based on the values of the parameters of its pdf. Its variance can be finite or infinite. Infinite variance random variables find applications in characterizing bursty data traffic. Therefore Pareto random variables are studied in this chapter. Since its study is a valuable review of elements of probability theory, it is introduced first.
